 ##  [Volterra Integral Equation](/volterra-integral-equation) 

  ##  [Volterra Integral Equation](https://mathlogic.quantumdictionary.io/volterra-integral-equation-0) 

  
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**Mathematics &amp; Logic Dictionary**

 
Definition

An integral equation in which the integration domain depends on the independent variable, typically of the form x(t)=f(t)+∫_{a}^{t} K(t,s)x(s) ds (Volterra of the second kind) or ∫_{a}^{t} K(t,s)x(s) ds=f(t) (first kind), embodying causal or history-dependent coupling.